UNIT 3 QUADRATIC FUNCTIONS SECTION 2 Solving Quadratic

UNIT 3 – QUADRATIC FUNCTIONS SECTION 2 – Solving Quadratic Functions

Solve by square roots • Read Textbook p. 268: Example 2 • Complete Quick Check 2 • a) 4 x 2 – 25 = 0 • 4 x 2 = 25 *Add 25 to both sides • x 2 = 25/4 *Divide by 4 • x = √ 25/4 • x = + 5 /2 *Take square root

Solve by square roots • Read Textbook p. 268: Example 2 • Complete Quick Check 2 • a) x = √ 25/4 *Take square root x = + 5 /2 • When you take a square root while solving, we do not know whether it is + or– Either could work when you plug it in for x. • You must use + when solving x 2 •

Solve by square roots • Read Textbook p. 268: Example 2 • Complete Quick Check 2 • b) 3 x 2 = 24 • x 2 = 8 *Divide by 3 • x = √ 8 • • x = + 2√ 2 c) x = + ½ *Take square root

Solve by square roots • Practice • Textbook p. 270: 7 – 18 all

COMPLEX NUMBERS • Read Textbook • p. 274 – 277: Examples 1, 2, 6, 7 • Practice: p. 278: 1 – 17 odd, 29 – 45 odd • Assignment: p. 278: 2 – 18 even, 30 – 46 even

Solve by Completing the Square • Read textbook p. 282: Example 1, 2 • Supplemental packet p. 39: Complete example 1 • Ex. 1) a) x 2 + 8 x + 16 = (x + 4)2 • b) x 2 + 10 x + ______ • Use (b/2)2 = (10/2)2 = 25 • x 2 + 10 x + 25 will factor into (x+5)2

Solve by Completing the Square • Read textbook p. 283: Example 3 • Supplemental packet p. 39: example 2 • x 2 + 4 x + 22= 0 • 1) x 2 + 4 x + ____ + 22 - ______ = 0 • What number completes the square? • x 2 + 4 x + _4_ + 22 - ______ = 0 • How do we balance it. • x 2 + 4 x + _4_ + 22 - _4_ = 0

Solve by Completing the Square • x 2 + 4 x + 22= 0 • step 2) x 2 + 4 x + _4_ + 22 - _4_ = 0 • Factor using (a + b)2 • (x + 2)2 + 18= 0 • Step 3) Solve • (x + 2)2 = -18 * Take square root • x + 2 = √-18 * Simplify the √-18 • x + 2 = + 3 i √ 2 * Subtract 2 • x = -2 + 3 i √ 2

Solve by Completing the Square • x 2 + 4 x + 22= 0 • Check using the PRIZM • Equation App (A) • F 2 – Polynomials • F 1 – Degree of 2 (degree is largest exponent) • Enter in each coefficient and EXE • You may have to change the settings to accept imaginary roots. Shift, Menu – Change COMPLEX MODE to a+bi

Solve by Completing the Square • Supplemental packet p. 39: example 3 • x 2 + 5 x – 10 = 0 • x 2 + 5 x + ____ - 10 - ______ = 0 • What number completes the square? • (5/2)2 = 25/4 • x 2 + 5 x + 25/4 - 10 - ______ = 0 • How do we balance it? • x 2 + 5 x + 25/4 - 10 - 25/4 = 0

Solve by Completing the Square • Supplemental packet p. 39: example 3 • x 2 + 5 x + 25/4 - 10 - 25/4 = 0 • FACTOR • (x + 5/2)2 - 65/4 = 0 • Solve (x + 5/2)2 = 65/4 * Take square root x + 5/2 = + √ 65/4 + √ 65/2 x = - 5/2 + √ 65/2 x + 5 /2 = CHECK ON PRIZM * Simplify the √ 65/4 * Subtract 5/2

Solve by Completing the Square • PRACTICE Supplemental packet p. 39: 1 -4 • Assignment Textbook: p. 285: 13 – 18 all

Solve by Completing the Square • Read textbook p. 284: Example 5 • Supplemental packet p. 40: example 4 • 5 x 2 + 10 x – 20 = 0 • 1) Factor 5 out of the first 2 terms. • 5(x 2 + 2 x) – 20 = 0 • What number completes the square? • 5(x 2 + 2 x + 1) – 20 _______ = 0

Solve by Completing the Square • Supplemental packet p. 40: example 4 • 5(x 2 + 2 x + 1) – 20 _____= 0 • How do we balance it? • 5(x 2 + 2 x + 1) – 20 - 5 = 0 • Why -5? • You added 1 inside the parentheses, but that is multiplied by 5, so we really just added in a 5, so balance it with -5.

Solve by Completing the Square • Supplemental packet p. 40: example 4 • 5(x 2 + 2 x + 1) – 20 - 5 = 0 • FACTOR: 5(x + 1)2 – 25 = 0 • SOLVE: 5(x + 1)2 = 25 • (x + 1)2 = 5 *Divide by 5 • x + 1 = + √ 5 • x = -1 + √ 5

Solve by Completing the Square • PRACTICE: Supplemental packet p. 40: 1 – 3 • Assignment: Textbook p. 285: 22 – 27 all

Solve by Quadratic Formula • Read textbook p. 283: Example 3 • Supplemental packet p. 39: example 2 • x 2 + 4 x + 22= 0 • 1) x 2 + 4 x + ____ + 22 - ______ = 0 • What number completes the square? • x 2 + 4 x + _4_ + 22 - ______ = 0 • How do we balance it. • x 2 + 4 x + _4_ + 22 - _4_ = 0